The invention relates to an automatic speed control mechanism for motor vehicles. Such mechanisms, sometimes called cruise controls, include a set-point generator in which a desired nominal speed is selected, either by the accelerator pedal or in a manual control and where a feedback controller maintains the vehicle at the desired speed within the range of the control loop. It is the position of the gas pedal or the manual control which sets the desired speed. As a consequence, in large domains of operation, especially at low and medium speeds and during accelerating processes, the engine operates with relatively high specific fuel consumption because the direct coupling of the accelerator throttle valve to the gas pedal does not allow for an optimization of the fuel consumption when automatic speed control is in operation.